Mann-Kendall Trend Test
Computes the Mann-Kendall test, used to detect a monotonic trend (upward or downward) in a time series without assuming the data are normal or the trend is linear. It sums the signs of all pairwise comparisons between values: if the series tends to rise over time, positive signs prevail. It's widely used in hydrology, climatology and environmental science to assess trends in long series. The S statistic becomes a z via the normal approximation, with a tie correction. Enter the series in chronological order.
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Mann-Kendall Trend Test
Computes the Mann-Kendall test, used to detect a monotonic trend (upward or downward) in a time series without assuming the data are normal or the trend is linear. It sums the signs of all pairwise comparisons between values: if the series tends to rise over time, positive signs prevail. It's widely used in hydrology, climatology and environmental science to assess trends in long series. The S statistic becomes a z via the normal approximation, with a tie correction. Enter the series in chronological order.
Is there a trend, even when the series misbehaves?
Environmental series — river flow, temperature, pollutant concentration — are rarely normal and almost never rise in a straight line. Even so, the question of whether there is a long-term trend remains. The Mann-Kendall test was made for this: it detects a monotonic trend without requiring any specific shape for the data.
The mechanism is to compare each value with all those that came after it and count the signs. Each time a later value is larger, it counts plus one; when smaller, minus one. If the series rises over time, positive signs dominate and the S statistic sits well above zero. Because S depends only on order, extreme values don't distort it, and a normal approximation converts S into a z score with a tie correction.
Enter the series in the order it was observed in time. The tool returns S and the z score, from which the p-value follows. Note that the test detects a trend but doesn't quantify it — to estimate the magnitude of the slope in an equally robust way, the natural companion is the Theil-Sen estimator.
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